The local-density approximation (LDA) is the central technical tool in modeling of quantum gases trapping potentials. It consists treating gas as an assembly independent mesoscopic fluid cells at equilibrium with a local chemical potential, and it justified when correlation length larger than size cells. LDA often regarded crude approximation, particularly ground state one-dimensional (1D) Bose...

For slowly varying fields the vacuum functional of a quantum field theory may be expanded in terms of local functionals. This expansion satisfies its own form of the Schrödinger equation from which the expansion coefficents can be found. For scalar field theory in 1+1 dimensions we show that this approach correctly reproduces the short-distance properties as contained in the counter-terms. We a...

Limit laws are proven by the contraction method for random vectors of a recursive nature as they arise as parameters of combinatorial structures such as random trees or recursive algorithms, where we use the Zolotarev metric. In comparison to previous applications of this method, a general transfer theorem is derived which allows us to establish a limit law on the basis of the recursive structu...

The modiied quark-meson coupling model, which features a density dependent bag constant and bag radius in nuclear matter, is checked against the EMC eeect within the framework of dynamical rescaling. Our emphasis is on the change in the average bag radius in nuclei, as evaluated in a local density approximation, and its implication for the rescaling parameter. We nd that when the bag constant i...

The electronic charge density and the expectation of any monoelectronic operator can be reconstructed by a density-weighted integral of the exchange-correlation hole. This property can be used to test and improve approximate holes that are not spherically averaged. As an example, we test the Becke–Roussel exhange-hole model in its nonspherical formulation on small atoms, finding that it accurat...

The nonmesonic weak decay of Λ hypernuclei using nonrelativistic nuclear matter is studied. As the basic building block we use the Polarization Propagator Method developed by Oset and Salcedo. It is shown that the exact calculation of exchange terms is required. Using the Local Density Approximation we evaluate the nonmesonic decay width for 12 Λ C and compare the result with a finite nucleus c...